Finite Group Databasebeta

← #11783622

Subgroups — #11783622

Order 1152.

773 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C2×#63657C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C2×#63554C211yesmaximal, characteristic, complemented
5C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
6#10589155C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#71582—31nomaximal
9#69907—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×#217C412yes—
14C3×#926—22no—
15C3×#926—22no—
16C2×C3×C4⋊Dic3C412yes—
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#63657C414yescomplemented
22C3×#830C414yescomplemented
23#63554—22no—
24Dic3×C3⋊C8—22no—
25C2×C3×#117—31no—
26C2×#926D311yescharacteristic
27C2×C3×C22⋊C8—31no—
28C2×#830—31no—
29C2×#830—31no—
30C2×#830—61no—
31C2×#830D311yescharacteristic
32C2×#815—31no—
33C2×C8×Dic3—31no—
34C2×#803—31no—
35C2×C4×C3⋊C8—31no—
36#4550—31no—
37#4550—31no—
38#4524—31no—
39#4524—31no—
40C24×C32C2×C411yescharacteristic
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2×C411yescharacteristic
46C22×C32×C4C2×C412yes—
47C22×C32×C4C2×C412yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3C2×C412yes—
50C22×C3×Dic3C2×C412yes—
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)C2×C412yes—
56C2×C3⋊(C3⋊C8)C2×C412yes—
57C3×#217—24no—
58C3×C4⋊Dic3—24no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3D412yes—
62C3×C4×Dic3D412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8C2×C412yes—
68C2×C3×C3⋊C8C2×C412yes—
69#1750—91noSylow
70C23×C3×C4—21no—
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C2×D311yescharacteristic
73C22×C3×C8—31no—
74C22×C3×C8—31no—
75C3×#117—62no—
76C3×#117—62no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C22⋊C4—32no—
79C2×C3×C42—31no—
80C2×C3×C42—31no—
81C2×#217Dic312yes—
82#926—22no—
83#926—22no—
84C2×C4⋊Dic3Dic312yes—
85C2×C4×Dic3C2×D311yescharacteristic
86C2×C4×Dic3C2×D311yescharacteristic
87C22×C3⋊C8—31no—
88C22×C3⋊C8—31no—
89C22×C3⋊C8—31no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—61no—
92C22×C3⋊C8—61no—
93C22×C3⋊C8C2×D311yescharacteristic
94C22×C3⋊C8C2×D311yescharacteristic
95C3×C22⋊C8—34no—
96#830—34no—
97#830—34no—
98#830—64no—
99#830Dic314yescomplemented
100#815—62no—
101C8×Dic3—62no—
102#803—62no—
103C4×C3⋊C8—62no—
104C23×C32—22no—
105C23×C32—21no—
106C23×C32—21no—
107C23×C32—22no—
108C23×C32C4212yes—
109C23×C32C22×C411yescharacteristic
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4C4212yes—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3C22⋊C414yes—
129C3⋊(C3⋊C8)—22no—
130C3⋊(C3⋊C8)—22no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—22no—
133C2×#117—31no—
134C2×C22⋊C8—31no—
135C2×C22⋊C8—91no—
136C2×#97—91no—
137C2×C4×C8—91no—
138#336—91no—
139#336—91no—
140C24×C3—21no—
141C24×C3C4×D311yescharacteristic
142C24×C3C2×Dic311yescharacteristic
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—21no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4—41no—
158C22×C3×C4—41no—
159C22×C3×C4—41no—
160C22×C3×C4—41no—
161C22×C3×C4C4×D311yescharacteristic
162C22×C3×C4C4×D312yes—
163C22×C3×C4C4×D312yes—
164C22×C3×C4C4×D312yes—
165C22×C3×C4C2×Dic311yescharacteristic
166C22×C3×C4C2×Dic312yes—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×Dic3C2×Dic312yes—
170C22×Dic3C2×Dic312yes—
171C2×C3×C8—32no—
172C2×C3×C8—32no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C3×C4⋊C4—64no—
178C3×C22⋊C4—64no—
179C3×C42—32no—
180C3×C42—32no—
181C3×C42—61no—
182C3×C42—61no—
183#217—24no—
184C4⋊Dic3—24no—
185C4×Dic3—21no—
186C4×Dic3—21no—
187C4×Dic3#6712yes—
188C4×Dic3#6712yes—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—32no—
194C2×C3⋊C8—32no—
195C2×C3⋊C8—32no—
196C2×C3⋊C8—32no—
197C2×C3⋊C8—62no—
198C2×C3⋊C8—62no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—121no—
208C2×C3⋊C8—121no—
209C2×C3⋊C8—121no—
210C2×C3⋊C8—121no—
211C2×C3⋊C8C2×Dic312yes—
212C2×C3⋊C8C2×Dic312yes—
213C22×C32—22no—
214C22×C32—22no—
215C22×C32—22no—
216C22×C32—42no—
217C22×C32—42no—
218C22×C32C2×C4211yescharacteristic
219C22×C32C2×C22⋊C411yescharacteristic
220C22×C32#11711yescharacteristic
221C22×C32#13112yes—
222C22×C32#13112yes—
223C32×C4—22no—
224C32×C4C4×D411yescharacteristic
225C32×C4C4×D411yescharacteristic
226C32×C4C4×D411yescharacteristic
227C32×C4C4×D411yescharacteristic
228C3×Dic3—24no—
229C3×Dic3—42no—
230C23×C4D3211yescharacteristic
231C22×C8—31no—
232C22×C8—31no—
233C22×C8—91no—
234C22×C8—91no—
235#117—62no—
236#117—62no—
237C2×C4⋊C4—32no—
238C2×C22⋊C4—32no—
239C2×C42—31no—
240C2×C42—31no—
241C22⋊C8—34no—
242C22⋊C8—94no—
243#97—182no—
244C4×C8—182no—
245C23×C3—24no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—21no—
251C23×C3—22no—
252C23×C3—22no—
253C23×C3—21no—
254C23×C3—22no—
255C23×C3—21no—
256C23×C3—41no—
257C23×C3—41no—
258C23×C3—42no—
259C23×C3C4×Dic312yes—
260C23×C3C4×Dic312yes—
261C23×C3C2×C4×D311yescharacteristic
262C23×C3C22×Dic311yescharacteristic
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—34no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4C4×Dic312yes—
295C2×C3×C4C4×Dic312yes—
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4#23511yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4#23711yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4C22×Dic311yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3#21714yes—
314C3×C8—62no—
315C3×C8—62no—
316C3⋊C8—22no—
317C3⋊C8—22no—
318C3⋊C8—62no—
319C3⋊C8—62no—
320C3⋊C8—62no—
321C3⋊C8—62no—
322C3⋊C8—122no—
323C3⋊C8—122no—
324C2×C32—42no—
325C2×C32C4×C22⋊C411yescharacteristic
326C2×C32#40511yescharacteristic
327C2×C32#40511yescharacteristic
328C2×C32#40812yes—
329C2×C32#43312yes—
330C24D3×Dic311yescharacteristic
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—32no—
336C22×C4—32no—
337C22×C4D3×Dic311yescharacteristic
338C22×C4D3×Dic312yes—
339C22×C4#62412yes—
340C22×C4C2×D3211yescharacteristic
341C2×C8—32no—
342C2×C8—32no—
343C2×C8—61no—
344C2×C8—61no—
345C2×C8—61no—
346C2×C8—61no—
347C2×C8—92no—
348C2×C8—92no—
349C2×C8—181no—
350C2×C8—181no—
351C2×C8—181no—
352C2×C8—181no—
353C4⋊C4—64no—
354C22⋊C4—64no—
355C42—32no—
356C42—32no—
357C42—61no—
358C42—61no—
359C22×C3—24no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3—44no—
374C22×C3—44no—
375C22×C3—42no—
376C22×C3—42no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3#87711yescharacteristic
380C22×C3D3×C22⋊C411yescharacteristic
381C22×C3#90112yes—
382C22×C3#90712yes—
383C22×C3C2×C4×Dic311yescharacteristic
384C22×C3C2×C4×Dic311yescharacteristic
385C22×C3#92611yescharacteristic
386C22×C3#94812yes—
387C22×C3#94812yes—
388C22×C3C2×#21711yescharacteristic
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—42no—
396C3×C4—64no—
397C3×C4—122no—
398C3×C4#67⋊C411yescharacteristic
399C3×C4#67⋊C411yescharacteristic
400C3×C4C4×#6711yescharacteristic
401C3×C4C4×#6711yescharacteristic
402C3×C4C4×#6711yescharacteristic
403C3×C4C4×#6711yescharacteristic
404C3×C4D4×Dic311yescharacteristic
405C3×C4D4×Dic311yescharacteristic
406Dic3—24no—
407Dic3—42no—
408C32#175011yescharacteristic, complemented, Sylow
409C23—22no—
410C23—22no—
411C23—21no—
412C23—21no—
413C23Dic3212yes—
414C23C2×D3×Dic311yescharacteristic
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—34no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4Dic3212yes—
428C2×C4C2×D3×Dic311yescharacteristic
429C2×C4#380411yescharacteristic
430C2×C4#380411yescharacteristic
431C2×C4C2×#62411yescharacteristic
432C2×C4D3×#6711yescharacteristic
433C2×C4D3×#6711yescharacteristic
434C8—62no—
435C8—62no—
436C8—182no—
437C8—182no—
438C2×C3—21no—
439C2×C3—22no—
440C2×C3—21no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3—44no—
444C2×C3—42no—
445C2×C3—42no—
446C2×C3#472012yes—
447C2×C3#472712yes—
448C2×C3Dic3×C22⋊C411yescharacteristic
449C2×C3#499711yescharacteristic
450C2×C3#499711yescharacteristic
451C2×C3#500012yes—
452C2×C3#510111yescharacteristic
453C2×C3#512211yescharacteristic
454C2×C3C4×#21711yescharacteristic
455C2×C3#523412yes—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—42no—
460C22—42no—
461C22#6381412yes—
462C22#6381512yes—
463C22C2×Dic3211yescharacteristic
464C22#6395511yescharacteristic
465C22D3×#21711yescharacteristic
466C4—22no—
467C4—64no—
468C4—122no—
469C4#6395211yescharacteristic
470C4#6395211yescharacteristic
471C4Dic3×#6711yescharacteristic
472C4Dic3×#6711yescharacteristic
473C3—21no—
474C3#6990711yescharacteristic, complemented
475C3#7158211yescharacteristic, complemented
476C2—42no—
477C2#1059105511yescharacteristic
478C2#1059105612yes—
479C2#1059105711yescharacteristic
480C2#1059114512yes—
481C2Dic3×#21711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1750
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×#63554C2semidirect
5. C2×Dic3×C3⋊C8C2semidirect
6. #10589155C2semidirect
7. #10589155C2semidirect
21. #63657C4semidirect
22. C3×#830C4semidirect
99. #830Dic3semidirect
408. C32#1750semidirect
474. C3#69907semidirect
475. C3#71582semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#9262
C2×#636572
C2×C3×#8302
C2×#635542
C2×Dic3×C3⋊C82
#105891552
#715823
#699073